Question

If `a_0=7` and `a_(n+1)=a_n+12` for `n>=0`, how do you find the values of `a_5`?

Answer 1

`a_5 = 55`

Explanation:

This recursive definition describes an arithmetic sequence with initial term `7` and common difference `12`.

The general term of an arithmetic sequence can be written:

`a_n = a+d(n-1)`

where `a` is the initial term and `d` the common difference.

So in our example, `a=7`, `d = 12` and:

`a_5 = a+d(5-1) = a+4d = 7+4*12 = 7+48 = 55`